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Patient-derived tumor organoids (PDTOs) are novel cellular models that maintain the genetic, phenotypic and structural features of patient tumor tissue and are useful for studying tumorigenesis and drug response. When integrated with advanced 3D imaging and analysis techniques, PDTOs can be used to establish physiologically relevant high-throughput and high-content drug screening platforms that support the development of patient-specific treatment strategies. However, in order to effectively leverage high-throughput PDTO observations for clinical predictions, it is critical to establish a quantitative understanding of the basic properties and variability of organoid growth dynamics. In this work, we introduced an innovative workflow for analyzing and understanding PDTO growth dynamics, by integrating a high-throughput imaging deep learning platform with mathematical modeling, incorporating flexible growth laws and variable dormancy times. We applied the workflow to colon cancer organoids and demonstrated that organoid growth is well-described by the Gompertz model of growth. Our analysis showed significant intrapatient heterogeneity in PDTO growth dynamics, with the initial exponential growth rate of an organoid following a lognormal distribution within each dataset. The level of intrapatient heterogeneity varied between patients, as did organoid growth rates and dormancy times of single seeded cells. Our work contributes to an emerging understanding of the basic growth characteristics of PDTOs, and it highlights the heterogeneity in organoid growth both within and between patients. These results pave the way for further modeling efforts aimed at predicting treatment response dynamics and drug resistance timing. 

Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on hypergraphs, in which each node takes one of the two types of different but constant fitness values. For the corresponding dynamics on conventional networks, under the birth-death process and uniform initial conditions, most networks are known to be amplifiers of natural selection; amplifiers by definition enhance the difference in the strength of the two competing types in terms of the probability that the mutant type fixates in the population. In contrast, we provide strong computational evidence that a majority of hypergraphs are suppressors of selection under the same conditions by combining theoretical and numerical analyses. We also show that this suppressing effect is not explained by one-mode projection, which is a standard method for expressing hypergraph data as a conventional network. Our results suggest that the modeling framework for structured populations in addition to the specific network structure is an important determinant of evolutionary dynamics, paving a way to studying fixation dynamics on higher-order networks including hypergraphs. 

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.